To find the percent depreciation of Ken's bike, we first need to calculate the amount of depreciation and then determine what percent that is of the original value.
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Calculate the amount of depreciation: \[ \text{Depreciation} = \text{Original Value} - \text{Current Value} = 460 - 320 = 140 \]
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Calculate the percent depreciation: \[ \text{Percent Depreciation} = \left(\frac{\text{Depreciation}}{\text{Original Value}}\right) \times 100 = \left(\frac{140}{460}\right) \times 100 \]
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Calculate the fraction and then the percentage: \[ \frac{140}{460} = 0.3043478261 \quad (\text{approximately}) \] Now, multiplying by 100 to get the percentage: \[ 0.3043478261 \times 100 \approx 30.43 \]
Thus, the value of Ken's bike has depreciated by approximately 30.43% over the past year.
In summary, about 30.4%.